Analysis and optimal boundary control of a nonstandard system of phase field equations
Please always quote using this URN:urn:nbn:de:0296-matheon-10665
- We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type.
Author: | Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels |
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URN: | urn:nbn:de:0296-matheon-10665 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2012/02/17 |
Release Date: | 2012/02/17 |
Tag: | Cahn--Hilliard systems; first-order necessary optimality conditions; nonlinear phase field systems; optimal boundary control; parabolic systems |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations |
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations | |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A15 Thermodynamics | |
Preprint Number: | 923 |